Stacks and the homotopy theory of simplicial sheaves.

Jardine, J.F.

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Higher monodromy.

Polesello, Pietro, Waschkies, Ingo (2005)

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$A^{1}$ -homotopy theory of schemes

Fabien Morel, Vladimir Voevodsky (1999)

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Riemann-Roch theorem for higher bivariant K-functors

Roni N. Levy (2008)

Annales de l’institut Fourier

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One defines a Riemann-Roch natural transformation from algebraic to topological higher bivariant K-theory in the category of complex spaces.

Classifying toposes and foliations

Ieke Moerdijk (1991)

Annales de l'institut Fourier

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For any etale topological groupoid $G$ (for example, the holonomy groupoid of a foliation), it is shown that its classifying topos is homotopy equivalent to its classifying space. As an application, we prove that the fundamental group of Haefliger for the (leaf space of) a foliation agrees with the one introduced by Van Est. We also give a new proof of Segal’s theorem on Haefliger’s classifying space $B Γ^{q}$ .